Elastic spherical shell impacted with an elastic barrier: A closed form solution

In this paper, the impact of a thin-walled elastic spherical shell with an elastic barrier is investigated. Hertzian and Reissner (membrane–bending deformation) theories were employed for the deformation equations. Due to the complexity of the equations a linearization of the equations was proposed and a closed form solution of the problem was obtained. Newtonian method is applied in order to obtain the impact force and the time duration. The closed-form solution enables one to parametrically study the impact and the related quantities. Finally the results from the analytical solution are validated by the finite element method and also are compared with the results presented in Young (2003). The comparison of the results reveals a good agreement. It is concluded that the proposed closed-form solution can be used to parametrically assess the impact of elastic spherical shells to elastic half space.